Reynolds number calculator

This free Reynolds number calculator computes the Reynolds number and the flow regime for a circular pipe, from either the velocity or the flow rate, with built-in fluid presets or a custom density and kinematic viscosity, a standard pipe-size picker and a metric or imperial toggle. The Reynolds number is the dimensionless ratio of inertial to viscous forces, the single best predictor of whether pipe flow is laminar, transitional or turbulent, and it sets the friction factor and the heat-transfer correlations that follow.

Method

For flow in a circular pipe,

Re = rho v D / mu = v D / nu

where rho is density (kg/m^3), v is mean velocity (m/s), D is internal diameter (m), mu is dynamic viscosity (Pa s) and nu = mu / rho is kinematic viscosity (m^2/s). If you have the volumetric flow rather than the velocity, v = 4Q / (pi D^2), so Re = 4Q / (pi D nu).

Conventional regime boundaries for pipe flow:

• Laminar: Re < 2300
• Transitional: 2300 < Re < 4000
• Turbulent: Re > 4000

These thresholds are conventional, not sharp, and transition depends on inlet conditions and disturbances. They trace back to Osborne Reynolds' 1883 dye experiments, which are worth reading if you have never seen the original.

Limits. The internal pipe diameter is the length scale here. For a non-circular duct the hydraulic diameter is used instead, which the rectangular duct pressure drop calculator evaluates for you. The Reynolds number here is the ordinary Newtonian one. The Studio uses the Metzner-Reed generalised Reynolds number for non-Newtonian fluids.

Inputs

• Fluid preset (density and viscosity) or a custom density and kinematic viscosity.
• Internal diameter D, typed or from the standard pipe-size picker.
• Velocity v, or the volumetric flow Q via the pipe velocity relation.

Outputs

• Reynolds number.
• Flow regime (laminar, transitional or turbulent).
• In the flow-rate mode, the mean velocity.

Kinematic viscosity and density of water

Liquid water at atmospheric pressure, from standard property tables (White, Fluid Mechanics, and the IAPWS correlations). The calculator's Water 10, 20 and 40 degrees C presets use the solver's built-in water correlations and agree with this table to rounding. For other temperatures pick Custom and enter the density and kinematic viscosity from this table.

Typical kinematic viscosities of common fluids

These are the representative values behind the calculator's preset dropdown, at the temperature shown. 1 cSt = 1 x 10^-6 m2/s. Fuels and oils vary with grade and temperature (ISO VG oils are defined by their viscosity at 40 degrees C, and diesel and petrol vary by blend and season), so for design work enter your datasheet value at operating temperature with the Custom option.

Reynolds number for water at 20 deg C, by pipe size and velocity

Straight arithmetic with Re = vD/nu at nu = 1.004 x 10^-6 m2/s (water at 20 degrees C), the same calculation the widget performs. Every entry is far above 4000, which is why ordinary water systems are practically always turbulent and laminar flow in practice belongs to viscous oils, small bores and very low velocities.

Worked example

Water at 20 degrees C (kinematic viscosity 1.004 x 10^-6 m^2/s) in a 50 mm pipe at 1.5 m/s:

Re = 1.5 x 0.05 / 1.004e-6 = 74,700

which is well into the turbulent range.

Frequently asked questions

What Reynolds number counts as laminar and what counts as turbulent?

For pipe flow the conventional bounds are laminar below 2300, transitional between 2300 and 4000, and turbulent above 4000, which are exactly the bounds this calculator reports. They are conventions rather than sharp lines, so carefully controlled flow can stay laminar higher, and disturbances can trip it earlier.

Do I enter dynamic or kinematic viscosity?

The calculator works with kinematic viscosity in m2/s. If your datasheet gives dynamic viscosity in Pa s (or mPa s), divide by the density in kg/m3 to get kinematic viscosity, since nu = mu/rho. The fluid presets already carry the right values.

Can I start from the flow rate instead of the velocity?

Yes. Switch to From flow rate mode, enter the flow in L/s (or gpm in imperial) and the internal diameter, and the calculator converts to mean velocity with v = 4Q/(pi D^2) and reports that velocity alongside the Reynolds number and regime.

Which diameter do I use?

The internal (bore) diameter of the pipe, not the nominal size. The built-in pipe-size picker fills the true internal diameter for Sch 10, 40, 80 and 160 sizes to ASME B36.10M. For a rectangular or annular duct the hydraulic diameter is the right length scale, which this single-pipe tool does not compute, but the rectangular duct calculator evaluates Re on D_h for you.

Does it work in imperial units?

Yes. The Metric (SI) / Imperial (US) toggle switches diameter to inches, velocity to ft/s and flow to gpm, converting the values you have already entered in place. Custom density and kinematic viscosity are always entered in SI units (kg/m3 and m2/s) in both systems.

Can I use it for air or another gas?

Yes, for the Reynolds number itself. Pick Custom and enter the gas's kinematic viscosity, about 1.5 x 10^-5 m2/s for air at 20 degrees C, since Re only needs viscosity, diameter and velocity. Compressible pressure-drop behaviour is a separate question, which the Studio's gas solver handles.

References

• Reynolds, O. (1883), "An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels", Philosophical Transactions of the Royal Society. doi.org/10.1098/rstl.1883.0029
• White, F. M., Fluid Mechanics, McGraw-Hill, for the regime conventions and the water property table.
• International Association for the Properties of Water and Steam (IAPWS), for the underlying water property correlations. The Studio's built-in water presets follow the same relations.
• Crane Co., Technical Paper No. 410: Flow of Fluids Through Valves, Fittings and Pipe, one of the tabulations behind the representative fluid properties above. These are indicative figures for a preset dropdown, so use your own datasheet value at operating temperature for design work. tp410.com

Related

• Darcy friction factor calculator
• Pipe pressure drop calculator
• Pipe velocity calculator
• Rectangular duct pressure drop calculator
• Open the Studio for full networks.